#randomwalk — Public Fediverse posts

`His initial intended uses were for linguistic analysis and other mathematical subjects like card shuffling, but both Markov chains and matrices rapidly found use in other fields.`

https://en.wikipedia.org/wiki/Stochastic_matrix#History

#AndreyMarkov #Markov #MarkovChain #MarkovModel #statistics #stochastic #stochasticProcess #randomWalk #statisticalPhysics #physics #inference #distribution #equilibrium #transitionRate #transitionMatrix #MarkovMatrix #stochasticMatrix #linearAlgebra #differentialEquation #equation

`His initial intended uses were for linguistic analysis and other mathematical subjects like card shuffling, but both Markov chains and matrices rapidly found use in other fields.`

https://en.wikipedia.org/wiki/Stochastic_matrix#History

#AndreyMarkov #Markov #MarkovChain #MarkovModel #statistics #stochastic #stochasticProcess #randomWalk #statisticalPhysics #physics #inference #distribution #equilibrium #transitionRate #transitionMatrix #MarkovMatrix #stochasticMatrix #linearAlgebra #differentialEquation #equation

`His initial intended uses were for linguistic analysis and other mathematical subjects like card shuffling, but both Markov chains and matrices rapidly found use in other fields.`

https://en.wikipedia.org/wiki/Stochastic_matrix#History

#AndreyMarkov #Markov #MarkovChain #MarkovModel #statistics #stochastic #stochasticProcess #randomWalk #statisticalPhysics #physics #inference #distribution #equilibrium #transitionRate #transitionMatrix #MarkovMatrix #stochasticMatrix #linearAlgebra #differentialEquation #equation

`His initial intended uses were for linguistic analysis and other mathematical subjects like card shuffling, but both Markov chains and matrices rapidly found use in other fields.`

https://en.wikipedia.org/wiki/Stochastic_matrix#History

#AndreyMarkov #Markov #MarkovChain #MarkovModel #statistics #stochastic #stochasticProcess #randomWalk #statisticalPhysics #physics #inference #distribution #equilibrium #transitionRate #transitionMatrix #MarkovMatrix #stochasticMatrix #linearAlgebra #differentialEquation #equation

`His initial intended uses were for linguistic analysis and other mathematical subjects like card shuffling, but both Markov chains and matrices rapidly found use in other fields.`

https://en.wikipedia.org/wiki/Stochastic_matrix#History

#AndreyMarkov #Markov #MarkovChain #MarkovModel #statistics #stochastic #stochasticProcess #randomWalk #statisticalPhysics #physics #inference #distribution #equilibrium #transitionRate #transitionMatrix #MarkovMatrix #stochasticMatrix #linearAlgebra #differentialEquation #equation

Just updated my #R #Package in #dev on #GitHub with another #RandomWalk this time from the #Logistic #Distribution with random_logistic_walk() See below :) #ggplot2 #tidydata

How about a #3D #Plot using #Plotly for a #NegativeBinomial #RandomWalk

Hot from the press, with Richard Mann
and @elva: 🐜 Random walks with spatial and temporal resets can explain individual and colony-level searching patterns in ants

https://royalsocietypublishing.org/doi/10.1098/rsif.2024.0149

#physics #ants #animalmovement #animabehaviour #randomwalk #behaviouralecology

A drunk man will find his way home, but a drunk bird may get lost forever.” What is this sentence about?

In 2D, the random walk is “recurrent”, i.e. you are guaranteed to go back to where you started; but in 3D, the random walk is “transient”, the opposite of “recurrent”. In fact, for the 2D case, that also means that you are guaranteed to go to ALL places in the world (the only constraint is, of course, time). [Think about why.]

Markov chains are also an important tool in modelling the real world, and so I feel like this is a good excuse for bringing it up.

At the end, I also compare this phenomenon to Stein’s paradox – in both cases, there is a cutoff between 2 and 3 dimensions, and they have similar intuitive explanation – is that a coincidence?

Random walks in 2D and 3D are fundamentally different

#MarkovChain #MarkovChains #Math #Mathematics #nowWatching #randomWalk #randomness #StochasticProcess #YouTube

A drunk man will find his way home, but a drunk bird may get lost forever.” What is this sentence about?

In 2D, the random walk is “recurrent”, i.e. you are guaranteed to go back to where you started; but in 3D, the random walk is “transient”, the opposite of “recurrent”. In fact, for the 2D case, that also means that you are guaranteed to go to ALL places in the world (the only constraint is, of course, time). [Think about why.]

Markov chains are also an important tool in modelling the real world, and so I feel like this is a good excuse for bringing it up.

At the end, I also compare this phenomenon to Stein’s paradox – in both cases, there is a cutoff between 2 and 3 dimensions, and they have similar intuitive explanation – is that a coincidence?

Random walks in 2D and 3D are fundamentally different

#MarkovChain #MarkovChains #Math #Mathematics #nowWatching #randomWalk #randomness #StochasticProcess #YouTube

A drunk man will find his way home, but a drunk bird may get lost forever.” What is this sentence about?

In 2D, the random walk is “recurrent”, i.e. you are guaranteed to go back to where you started; but in 3D, the random walk is “transient”, the opposite of “recurrent”. In fact, for the 2D case, that also means that you are guaranteed to go to ALL places in the world (the only constraint is, of course, time). [Think about why.]

Markov chains are also an important tool in modelling the real world, and so I feel like this is a good excuse for bringing it up.

At the end, I also compare this phenomenon to Stein’s paradox – in both cases, there is a cutoff between 2 and 3 dimensions, and they have similar intuitive explanation – is that a coincidence?

Random walks in 2D and 3D are fundamentally different

#MarkovChain #MarkovChains #Math #Mathematics #nowWatching #randomWalk #randomness #StochasticProcess #YouTube